# 臺灣博碩士論文加值系統

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 在本論文中，我們提出重建微中子源角分佈的方法。通過重建太陽微中子角分佈的經驗，我們可以應用相同方法重建大氣微中子、月球微中子、地球微中子和太陽大氣微中子等的角分佈上。我們探討微中子與偵測器內部電子間的彈性散射，從而得出電子反彈動量的大小與角度分佈。數學上我們看出電子反彈動量分佈其實是原始微中子角分佈的雷冬變換。在我們的例子中，上述雷冬變換是一個二維特例。為了重建微中子角分佈，我們需要找雷冬變換的反變換。文獻 [5]中提到找反變換的幾種方法，本篇論文我們利用球諧函數展開的方法找到反變換。
 In this thesis, we have presented the way to reconstruct the angular distribution of extended neutrino sources. By reconstructing the angular distribution of solar neutrinos, we can do the same for other extended neutrino sources such as atmospheric neutrinos, lunar neutrinos, geoneutrinos, and solar atmospheric neutrinos.We focused on the elastic scattering process between the neutrino and the electron inside the detector to obtain data on the recoil momentum spectrum. We know that the recoil momentum spectrum is the Radon transform of the original distribution function. In our case, the recoil momentum spectrum is a special case of the Radon transform of the original neutrino angular distribution. So, to reconstruct the angular distribution, we need to invert the Radon transform. There are several ways to inverse the Radon transform mentioned in [5], here we reconstruct the original neutrino angular distribution by expanding the angular distribution function and its Radon transform into spherical harmonics.
 摘要............................................................................................ iAbstract....................................................................................... iiTable of Contents ....................................................................... iiiList of Figures .............................................................................. ivList of Tables................................................................................ v1 Overview about neutrinos ....................................................... 11.1 Neutrino discovery history ................................................... 11.2 Solar neutrino........................................................................ 41.2.1 Motivations for the solar neutrino study ...........................71.2.2 Standard solar models ....................................................... 91.2.3 Solar neutrino detection experiments................................ 121.3 Thesis organization ................................................................ 222 Theoretical framework.............................................................. 252.1 ν−e elastic scattering ............................................................. 252.2 Recoil momentum spectrum .................................................. 272.3 Radon transform and its inverse ............................................ 292.4 Expansion into spherical harmonics ....................................... 313 Reconstructing the angular distribution of extended neutrino source via inverse Radon transform..................................................................................... 343.1 Computing the angular distribution of 8B neutrino.............. 343.2 Expansion into the spherical harmonics ................................ 373.3 Results..................................................................................... 404 Conclusion ................................................................................. 44Appendix A 附錄標題 .................................................................. 47
 1] W. C. Haxton, B. R. Holstein, “Neutrino physics”, Am. J. Phy. 68, 1532 (2000).[2] C. Giunti and C. W. Kim, “Fundamentals of Neutrino Physics and Astrophysics”, (2007).[3] F. An et al., “Neutrino physics with JUNO”, J. Phys. G 43, 030401 (2016).[4] G. L. Lin, T. T. L. Nguyen, M. Spinrath, T. C. Wang, T. D. H. Van, “Taking Neutrino Pictures via Electrons” (2022) [arXiv:2201.06733 [hepph]]. This paper has been accepted by JCAP.[5] P. Gondolo, “Recoil momentum spectrum in directional dark matter detectors”, Phys. Rev. D 66, 103513 (2002).[6] J. N. Bahcall, M. H. Pinsonneault, S. Basu“Solar Models: current epoch and time dependences, neutrinos, and helioseismological properties”, Astrophys.J 555, 9901012 (2001).[7] D. D’Angelo et al.,“Recent Borexino results and prospects for the near future”, EPJ Web of Conferences 126, 02008 (2016).[8] N. Vinyoles et al., “A new generation of standard solar models”, The Astrophysical Journal 835, 2 (2017).[9] V. Antonelli, L. Miramonti, C. PeñaGaray, and A. Serenelli, “Solar Neutrinos”, (2012).[10] D. Besson, D. Cowen, M. Selen, and C. Wiebusch, “Neutrinos”, 96, 25, 1420114202, (1999).[11] R. Davis, Jr., D. S. Harmer, and K. C. Hoffman, “Search for Neutrinos from the Sun”, Phys. Rev. Lett. 20, 1205 (1968).[12] W. Hampel et al.,“GALLEX solar neutrino observations: results for GALLEX IV ”, Phys. Lett. B 447, 127133 (1999).[13] J. N. Abdurashitov et al., “Measurement of the solar neutrino capture rate with gallium metal. III: Results for the 2002–2007 datataking period ”, Phys. Rev. C 80, 015807 (2009).[14] K. S. Hirata et al., “Observation of 8B solar neutrinos in the KamiokandeII detector ”, Phys. Rev. Lett. 63, 16 (1989).[15] K. Abe et al., “Solar Neutrino Measurements in SuperKamiokandeIV ”, Phys. Rev. D 94, 052010 (2016).[16] H. H. Chen, “Direct Approach to Resolve the SolarNeutrino Problem ”, Phys. Rev. Lett. 55, 1534 (1985).[17] A. Gando et al., “Measurement of the 8B Solar Neutrino Flux with the KamLAND Liquid Scintillator Detector”, Phys. Rev. C 84, 035804 (2011).[18] A. Gando et al., “7Be Solar Neutrino Measurement with KamLAND”, Phys. Rev. C 92, 055808 (2015).[19] W. J. Marciano, Z. Parsa, “NeutrinoElectron Scattering Theory ”, J. Phys. G 29, 2629-2645 (2003).[20] E. Vitagliano, I. Tamborra, G. Raffelt, “Grand Unified Neutrino Spectrum at Earth: Sources and Spectral Components”, Rev. Mod. Phys. 92, 45006 (2020).[21] M. Agostini et al., “Comprehensive measurement of ppchain solar neutrinos ”, Nature 562, 7728, 505510 (2018).[22] G. D. O. Gann, K. Zuber, D. Bemmerer and A. Serenelli, “The Future of Solar Neutrinos”, Ann. Rev. Nucl. Part. Sci. 71, 491528 (2021).[23] E. Vitaglinao, J. Redondo and G. Rafelt “Solar neutrino flux at keV energies”, JCAP 1712 12, 010 (2017).
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